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Chapter 5: Problem 16
Add or subtract as indicated. $$\left(x^{4}-7 x y-5 y^{3}\right)-\left(6 x^{4}-3 x y+4 y^{3}\right)$$
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Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)(x-3)\) b. \((x+5)(x-5)\)
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. There are many exponential expressions that are equal to \(36 x^{12},\) such as \(\left(6 x^{6}\right)^{2},\left(6 x^{3}\right)\left(6 x^{9}\right), 36\left(x^{3}\right)^{9},\) and \(6^{2}\left(x^{2}\right)^{6}\)
In Exercises \(85-86,\) the variable \(n\) in each exponent represents a natural Number. Divide the polynomial by the monomial. Then use polynomial multiplication to check the quotient. $$\frac{12 x^{15 n}-24 x^{12 n}+8 x^{3 n}}{4 x^{3 n}}$$
Use a vertical format to find each product. $$\begin{array}{r}7 x^{3}-5 x^{2}+6 x \\\3 x^{2}-4 x \\\\\hline\end{array}$$
In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{20 x^{7} y^{4}-15 x^{3} y^{2}-10 x^{2} y}{-5 x^{2} y}$$
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